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AppDefInt - Math 16B Kouba Applications of Definite...

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Unformatted text preview: Math 16B Kouba Applications of Definite Integrals 15 2t + 3 a.) What is the tree’s growth rate when t = 0 years 7 b.) What is the tree’s growth rate when t = 9 years 7 c.) What is the height of the tree at the end of the 12-year growth period 7 1.) A palm tree is growing at the rate of ft./yr., where t is in years for 0 S t S 12. 2.) You go on a bike ride. Assume your velocity at time 75 (hours) is t- \/ t2 + 3 miles / hour for 0 S t g 5 . a.) What is your velocity when t = 1 hour 7 b.) What is your velocity when t = 3 hours 7 c.) What is the total distance traveled for O S t g 5 7 3.) Water is leaking from a large tank at the rate of (1 /4)t2 gal. /hr., where t is given in hours for t Z 0 . a.) What is the leakage rate when t = 1 hour 7 b.) What is the leakage rate when t = 5 hours 7 c.) What is the total amount of water which leaks from the tank for 0 g t S 6 7 d.) If the tank initially holds 100 gallons, how long will it take for the tank to become empty 7 4.) A thin wire lies along the {B—aXlS from :L' = 0 to :r = 27r cm. It’s density at a: is given to be 3 + sin 2:5 grams/ cm. a.) What is the wire’s density at :r : 0 cm. 7 b.) What is the wire’s density at :r = 71/4 cm. 7 c.) What is the wire’s density at a: = 77r/4 cm. 7 d.) What is the total mass of the wire 7 e.) What is the mass of the wire from a; = 7T/2 cm. to m : 7r cm. 7 ...
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